code: def test_decomp_1():
      # All prime decompositions in cyclotomic fields are in the "easy case,"
      # since the index is unity.
      # Here we check the ramified prime.
      T = Poly(cyclotomic_poly(7))
      raises(ValueError, lambda: prime_decomp(7))
      P = prime_decomp(7, T)
      assert len(P) == 1
      P0 = P[0]
      assert P0.e == 6
      assert P0.f == 1
      # Test powers:
      assert P0**0 == P0.ZK
      assert P0**1 == P0
      assert P0**6 == 7 * P0.ZK
  
imports: from math import prod
  from sympy import QQ, ZZ
  from sympy.abc import x, theta
  from sympy.ntheory import factorint
  from sympy.ntheory.residue_ntheory import n_order
  from sympy.polys import Poly, cyclotomic_poly
  from sympy.polys.matrices import DomainMatrix
  from sympy.polys.numberfields.basis import round_two
  from sympy.polys.numberfields.exceptions import StructureError
  from sympy.polys.numberfields.modules import PowerBasis, to_col
  from sympy.polys.numberfields.primes import prime_decomp, _two_elt_rep, _check_formal_conditions_for_maximal_order
  from sympy.testing.pytest import raises
label_desc: Use image node_id 4 for calling a global function with example usage: test_decomp_1() without return types